Strongly mixed random errors in Mann's iteration algorithm for a contractive real function
Probability
2017-01-31 v1
Abstract
This work deals with the Mann's stochastic iteration algorithm under strong mixing random errors. We establish the Fuk-Nagaev's inequalities that enable us to prove the almost complete convergence with its corresponding rate of convergence. Moreover, these inequalities give us the possibility of constructing a confidence interval for the unique fixed point. Finally, to check the feasibility and validity of our theoretical results, we consider some numerical examples, namely a classical example from astronomy.
Cite
@article{arxiv.1701.08737,
title = {Strongly mixed random errors in Mann's iteration algorithm for a contractive real function},
author = {Hassina Arroudj and Idir Arab and Abdelnasser Dahmani},
journal= {arXiv preprint arXiv:1701.08737},
year = {2017}
}